Journal ArticleDOI
Discrimination among some parametric models
TLDR
In this paper, the error model is transformed and reparameterized to induce regular estimation on the boundary with one or both degrees of freedom infinite, leading to bivariate score tests for normal, extreme value and logistic special cases as well as an evaluation of these models within a more general framework.Abstract:
SUMMARY Linear models, with errors that follow the distribution of the logarithm of an F statistic, are shown to include a number of common statistical models as special cases. The error model is transformed and reparameterized to induce regular estimation on the boundary with one or both degrees of freedom infinite. This leads to bivariate score tests for normal, extreme value and logistic special cases as well as an evaluation of these models within a more general framework. In particular, the test for normality is found to reduce to the usual tests based on sample skewness and kurtosis. Sample sizes are given for pairwise discrimination among some specific models. Applications are indicated.read more
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Journal Article
A class of distributions which includes the normal ones
TL;DR: In this paper, a nouvelle classe de fonctions de densite dependant du parametre de forme λ, telles que λ=0 corresponde a la densite normale standard.
Journal ArticleDOI
A class of rank test procedures for censored survival data
TL;DR: In this article, a class of linear rank statistics is proposed for the k-sample problem with right-censored survival data, which contains as special cases the log rank test (Mantel, 1966; Cox, 1972) and a test essentially equivalent to Peto & Peto's (1972) generalization of the Wilcoxon test.
Journal Article
A class of rank test procedures for censored survival data
TL;DR: A class of linear rank statistics is proposed for the k-sample problem with rightcensored survival data andMartingale theory is used to establish asymptotic normality of test statistics under the null hypotheses considered, and to derive expressions for asymPTotic relative efficiencies under contiguous sequences of alternative hypotheses.
Book
Statistical Size Distributions in Economics and Actuarial Sciences
Christian Kleiber,Samuel Kotz +1 more
TL;DR: The Statistical Size Distribution in Economics and Actuarial Sciences (SDFIS) as discussed by the authors is a collection of parametric models that deal with income, wealth, and related notions.
Journal ArticleDOI
The exponentiated Weibull family: a reanalysis of the bus-motor-failure data
TL;DR: In this paper, the Weibull family with survival function exp{-(y/σ)α, for α > 0 and y ≥ 0, is generalized by adding an additional shape parameter θ.
References
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Continuous univariate distributions
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Journal ArticleDOI
A Generalization of the Gamma Distribution
TL;DR: In this paper, a generalization of the gamma distribution is proposed, which is based on Liouville's extension to Dirichlet's integral formula, and the moment generating function is shown, and cumulative probabilities are related directly to the incomplete gamma function.
Journal ArticleDOI
Further Results on Tests of Separate Families of Hypotheses
TL;DR: In this article, a modification of the Neyman-Pearson maximum-likelihood ratio test was suggested for this problem, and general comments on the formulation of the problem, a general large sample form for the test, and, finally, a number of examples.
Further results on tests of separate families of hypotheses
TL;DR: In this paper, a modification of the Neyman-Pearson maximum-likelihood ratio test was suggested for this problem, and general comments on the formulation of the problem, a general large sample form for the test, and, finally, a number of examples.